Program Trigs;
{ Gerson Washiski Barbosa - Dec/2007 }
{ Trigonometric and inverse trigonometric functions (17-digit accuracy) }
{ To be compiled in TurboBCD (Turbo Pascal v3.02) }
{ Running times: Sin, Cos: 160.5 us; Tan: 321.0 us @ 500 MHz }
{ All angles in DEGREES }
var x: Real;
txt: Text;
function Sqrt(x: Real): real;
var sq, t: Real;
begin
if x<>0 then
begin
sq:=x/2;
repeat
t:=sq;
sq:=(sq+x/sq)/2
until sq=t;
Sqrt:=sq
end
else
Sqrt:=0
end;
function Intg(x: Real): Real;
var r: Real;
begin
r:=Int(x);
if x<0 then r:=r-1;
Intg:=r
end;
function Mdl(x, y: Real): Real;
begin
Mdl:=x-y*Intg(x/y)
end;
function Sign(x: Real): Integer;
begin
if x<>0 then
Sign:=Trunc((x)/Abs(x))
else
Sign:=0
end;
function Sin(x: Real): Real;
const A = 5.81776417331443192E-03;
B = -3.28183761370851117E-08;
C = 5.55391614470475312E-14;
D = -4.47571324262354212E-20;
E = 2.10398182046943194E-26;
F = -6.47383342002944734E-33;
G = 1.40457976326925111E-39;
H = -2.25584840859272218E-46;
var sn,x2: Real;
begin
x:=Mdl(x,360);
if x>90
then
if x<270
then
x:=180-x
else
x:=x-360;
x2:=x*x;
sn:=x*(A+x2*(B+x2*(C+x2*(D+x2*(E+x2*(F+x2*(G+H*x2)))))));
Sin:=sn*(3-4*sn*sn)
end;
function Cos(x: Real): Real;
begin
Cos:=Sin(90-x)
end;
function Tan(x: Real): Real;
begin
if Mdl(x,180)<>90
then
Tan:=Sin(x)/Cos(x)
else
Tan:=Sign(x)*9.99999999999999999E+49
end;
function ArcTan(x: real): Real;
const PI_2 = 1.57079632679489662E+00; { pi/2 }
PI_6 = 0.52359877559829887E+00; { pi/6 }
SQR3 = 1.73205080756887729E+00; { sqrt(3) }
TLS3 = 2.67949192431122706E-01; { 2 - sqrt(3) }
R2D = 5.72957795130823209E+01; { 180/pi }
A = 1.00000000000000000E+00;
B = -3.33333333333333320E-01;
C = 1.99999999999969080E-01;
D = -1.42857142845613967E-01;
E = 1.11111109453593870E-01;
F = -9.09089712757808854E-02;
G = 7.69182100185790154E-02;
H = -6.65496746226271243E-02;
I = 5.71652168403095978E-02;
J = -3.95856057285009705E-02;
var at, k1, k2, x2: real;
s1, s2: integer;
begin
s1:=Sign(x);
x:=Abs(x);
if x<1 then
begin
s2:=1;
k1:=0
end
else
begin
x:=1/x;
s2:=-1;
k1:=PI_2
end;
if x>TLS3
then
begin
x:=(x*SQR3-1)/(x+SQR3);
k2:=PI_6
end
else
k2:=0;
x2:=x*x;
at:=x*(A+x2*(B+x2*(C+x2*(D+x2*(E+x2*(F+x2*(G+x2*(H+x2*(I+J*x2)))))))));
ArcTan:=(k1+s2*(k2+at))*s1*R2D
end;
function ArcSin(x: real): real;
begin
if Abs(x)<=1
then
if Abs(x)<1
then
ArcSin:=ArcTan(x/(Sqrt(1-x*x)))
else
ArcSin:=Sign(x)*90
else
begin
Write(^G);
WriteLn('ArcSin Error')
end;
end;
function ArcCos(x: real): real;
begin
if Abs(x)<=1
then
if Abs(x)<1
then
ArcCos:=2*ArcTan(Sqrt((1-x)/(1+x)))
else
ArcCos:=90*(1-x)
else
begin
Write(^G);
WriteLn('ArcCos Error')
end;
end;
begin
ClrScr;
Assign(txt,'OUTPUT.TXT');
Rewrite(txt);
x:=-180;
repeat
if Trunc(x) Mod 60 = 0 then
begin
WriteLn(txt);
WriteLn(txt,' x',' ':11,'Sin(x)',' ':18,'Cos(x)',' ':18,'Tan(x)');
WriteLn(txt)
end;
WriteLn(txt,x:4:0,' ',Sin(x):21:18,' ',Cos(x):21:18,' ',Tan(x));
x:=x+1
until x>179;
WriteLn(txt);
x:=-1;
WriteLn(txt,' x',' ':9,'ArcSin(x)',' ':16,'ArcCos(x)',' ':16,'ArcTan(x)');
WriteLn(txt);
repeat
WriteLn(txt,x:6:1,' ',ArcSin(x):22:18,' ',ArcCos(x):22:18,' ',ArcTan(x):22:18);
x:=x+0.1
until x>1;
x:=-150;
repeat
if x<>0 then WriteLn(txt,x:6:1,' ------------ ------------ ',ArcTan(x):22:18);
x:=x+10
until x>150;
WriteLn(txt);
WriteLn(txt,' ArcSin(ArcCos(ArcTan(Tan(Cos(Sin(9)))))) = ',ArcSin(ArcCos(ArcTan(Tan(Cos(Sin(9)))))):20:18);
Close(txt)
end.
Sample output
x Sin(x) Cos(x) Tan(x)
-151 -0.484809620246337029 -0.874619707139395801 5.54309051452768917E-01
-150 -0.500000000000000001 -0.866025403784438647 5.77350269189625766E-01
-149 -0.515038074910054210 -0.857167300702112288 6.00860619027560414E-01
59 0.857167300702112288 0.515038074910054210 1.66427948235051791E+00
60 0.866025403784438647 0.500000000000000001 1.73205080756887729E+00
61 0.874619707139395801 0.484809620246337029 1.80404775527142394E+00
89 0.999847695156391238 0.017452406437283513 5.72899616307594247E+01
90 1.000000000000000000 0.000000000000000000 9.99999999999999999E+49
91 0.999847695156391238 -0.017452406437283513 -5.72899616307594247E+01
134 0.719339800338651138 -0.694658370458997285 -1.03553031379056951E+00
135 0.707106781186547523 -0.707106781186547523 -1.00000000000000000E+00
136 0.694658370458997285 -0.719339800338651138 -9.65688774807074045E-01
x ArcSin(x) ArcCos(x) ArcTan(x)
-1.0 -90.000000000000000000 180.000000000000000000 -45.000000000000000300
-0.9 -64.158067236832871500 154.158067236832871000 -41.987212495816659900
-0.8 -53.130102354155979000 143.130102354155979000 -38.659808254090090300
0.0 0.000000000000000000 90.000000000000000600 0.000000000000000000
0.1 5.739170477266786350 84.260829522733213200 5.710593137499642520
0.2 11.536959032815487700 78.463040967184512000 11.309932474020213100
0.4 23.578178478201830900 66.421821521798168400 21.801409486351811500
0.5 29.999999999999999800 59.999999999999999600 26.565051177077989100
0.6 36.869897645844021100 53.130102354155978200 30.963756532073521100
-150.0 ---------- ------------ -89.618033795270974600
-140.0 ---------- ------------ -89.590751391965061500
10.0 ---------- ------------ 84.289406862500357400
20.0 ---------- ------------ 87.137594773888252600
ArcSin(ArcCos(ArcTan(Tan(Cos(Sin(9)))))) = 8.999999999996491040